How high does the lending rate in the euro zone have to be before an arbitrageur would not consider borrowing dollars,trading for euro at the spot,investing in the euro zone and hedging with a short position in the forward contract? $$\begin{array} { r c c c c } & \text { Bid } & \text { Ask } & \text { Borrowing } & \text { Lending } \ \boldsymbol { s } _ { 0 } ( \$ / € ) & \$ 1.40 - € 1.00 & \$ 1.43 - € 1.00 & \text { i\$ } 4.20 \% \mathrm { APR } & 4.10 \% \mathrm { APR } \ F _ { 360( \$ / € ) } & \$ 1.44 - € 1.00 & \$ 1.49 - € 1.00 & \text { i€ } & \end{array}$$ A)The bid-ask spreads are too wide for any profitable arbitrage when i_€ 0 B)3.48% C)?2.09% D)none of the options

Question

How high does the lending rate in the euro zone have to be before an arbitrageur would not consider borrowing dollars,trading for euro at the spot,investing in the euro zone and hedging with a short position in the forward contract? $$\begin{array} { r c c c c } & \text { Bid } & \text { Ask } & \text { Borrowing } & \text { Lending } \ \boldsymbol { s } _ { 0 } ( \$ / € ) & \$ 1.40 - € 1.00 & \$ 1.43 - € 1.00 & \text { i\$ } 4.20 \% \mathrm { APR } & 4.10 \% \mathrm { APR } \ F _ { 360( \$ / € ) } & \$ 1.44 - € 1.00 & \$ 1.49 - € 1.00 & \text { i€ } & \end{array}$$ A)The bid-ask spreads are too wide for any profitable arbitrage when i_€> 0 B)3.48% C)?2.09% D)none of the options

Quizplus · Accepted Answer

The arbitrage strategy involves borrowing dollars, converting them to euros at the spot rate, investing in the euro zone, and hedging the investment with a short position in the forward contract. The profit of the strategy is the difference between the euro zone interest rate and the dollar borrowing rate, minus the cost of the forward contract.

Let's calculate the profit of the strategy:
Profit = (Euro zone interest rate - Dollar borrowing rate) - (Forward rate - Spot rate)/Spot rate

We want to find the euro zone interest rate at which the profit becomes zero, i.e., when the cost of the forward contract equals the interest rate differential.

0 = (Euro zone interest rate - Dollar borrowing rate) - (Forward rate - Spot rate)/Spot rate

Euro zone interest rate = Dollar borrowing rate + (Forward rate - Spot rate)/Spot rate

Euro zone interest rate = 4.20% + (1.49 - 1.43)/1.43 = 4.20% + 0.042 = 4.242%

Therefore, the lending rate in the euro zone has to be at least 4.242% for the arbitrageur not to consider borrowing dollars and investing in the euro zone. The closest answer option is B) 3.48%, which is less than 4.242%, so it is not a high enough rate to deter the arbitrageur.

How High Does the Lending Rate in the Euro Zone